Motorcycle pulls in BEDE directions when driving strong. angular tires?

Hello together, after hours of searching in the inet without any real success, I decided to open up a new topic. I am currently looking for a motorcycle and would like to buy a used machine. Last week I drove a motorcycle test. (FZ6N s2 approx.10.000 km) however, the motorcycle pulled in the respective direction of the steering. It turned out that the tyre pressure was too low. After another test drive with correct tyre pressure, the The problem is much lower. However, if you are a little more distracted, the same effect has occurred again: you have to hold on to the handlebar, because otherwise it will steer further into the curve. (hope is to understand). The dealer said that the previous owner had gone “a lot straight ahead” and with new tyres the problem had been solved and there were no more concerns. The tyres of the motorcycle are already close to the wear limit and about 4.5 years old. Now my question: Can it be actually be that this effect occurs only because of the (angular) driven tires? or would another problem be in question? (e.g. steering head bearing, swing) Thanks a lot and LG